1. Astro 201: Sept. 2, 2010 Do on-line practice quiz #2 (see d2l) Homework #2: posted on web page Today: – Ptolemy V. Copernicus; retrograde motion – Galileo – Astronomical basis for calendars – Tycho, Kepler, Newton

2. Despite Aristarchus, for 2000 years, a GEOCENTRIC model of the Universe was favored EARTH at the center STARS affixed to the celestial sphere Moon, Planets and the Sun are between the EARTH and STARS

3. PTOLEMY 90-168 AD Ptolemy’s ALMAGEST was translated into Latin in 1496 GEOCENTRIC: Earth at center

4. Copernicus (1473-1543) Heliocentric Model: Sun at the center

5. In order to understand the motion of the planets in the sky Ptolemy’s model had to be modified In terms of the heliocentric model, the planets orbit the Sun in ellipses, not circles Retrograde motion of the planets with respect to the stars required EPICYCLES Ptolemy’s Epicycles

6. Ecliptic the fact that the planets orbit the Sun in a plane means that they always appear to lie on a great circle on the sky, called the ecliptic

7. Retrograde motion The planets sometimes appear to be traveling west to east, unlike the stars and Sun which always go east to west Next slide: animation Astronomy Picture of the Day for Dec. 20, 2001. Jupiter and Saturn showing retrograde motion. Combining 23 pictures taken at 2 week intervals from June 2000 - May 2001. Planet = “wanderer”

9. Ptolemy’s explanation for retrograde motion of the planets

11. Earth Equant Epicycle Deferent The planet moves along its epicycle as the epicycle moves along the deferent around the Earth. To make the observations as accurate as possible, it was necessary to place the Earth slightly off center of the orbits, but to preserve symmetry that meant that there was an equal place (“Equant”) opposite the Earth from the center. The combined motion of the planet and the resulting retrograde motion are shown. Earth Off Center

12. Copernicus’ explanation for retrograde motion

13. Copernicus: “On the Revolution of the Heavenly Spheres” Published at the time of his death, in 1543 Major Conclusions: 1.The planets orbit the Sun 2. The apparent daily motion of the Sun and stars is the result of the Earth’s rotation 3.The stars are much farther away than the Sun

14. Heliocentric model: distance from Sun to stars must be much greater than distance from Sun to Earth. Since Earth orbits Sun, stars should show parallax (a shift in apparent position) over the course of half a year.

15. Implication: distance to stars is several thousand times Earth – Sun distance. OBSERVATION: Parallax of stars is TOO SMALL to be seen by the naked eye. Not observed until 1800s.

16. Parallax Unit of distance: the PARSEC A star which is one parsec from Earth shows a parallax of one arcsecond Remember: 360 degrees in a circle, 60 arcminutes per degree, 60 arcseconds per arcminute

17. Reactions to Copernicus : On March 5, 1616, Copernicus' work was banned from being taught and discussed by the Congregation of the Index "until corrected." It stayed on this list of prohibited books and teachings until 1822. Martin Luther (1483-1546): [Copernicus] “is a fool who wishes to reverse the entire scheme of astronomy; but sacred scripture tells us that Joshua commanded the Earth to stand still, not the Sun.” Giordano Bruno (1548-1600): burned at the stake for advocating that stars are suns in their own right, and that there is a plurality of worlds like the Earth.

18. v. 1.0 v. 2.0 v. 3.0 Cosmological Models: Version 1.0: “Superdome” model Version 2.0: Geocentric model Version 3.0: Heliocentric model

19. Which is “right”? Occam's Razor: Pluralitas non est ponenda sine neccesitate "plurality should not be posited without necessity." Given a set of otherwise equivalent models of a phenomenon, the simplest one is the best. Keep it simple, stupid.

20. English philosopher from Ockham Franciscan Monk Got into trouble with the Pope for advocating “apostolic poverty” Died of the Black Death while in exile Advocated Epistomological Parsimony c.f. Ontological parsimony Epistomology = theory of knowledge Ontology = what exists? William of Occam 1285-1349

21. 1610 “Siderius Nuncius” (The Starry Messenger) “Spots” on the Sun; the Sun rotates The Moon has mountains, craters, rocky surface with imperfections The “planet” Jupiter is not a pinpoint star – but a disc in the sky WITH MOONS that orbit it Venus has “PHASES” like the MOON Galileo Galilei (1564 – 1642) Italian First to use a telescope to look at the sky

22. Spots on the Sun The Sun rotates Eventually went blind Galileo Galilei (1564 – 1642)

23. The Moon Has Mountains and Valleys Galileo Galilei (1564 – 1642)

24. Phases of Venus Galileo observed that Venus showed phases entirely like those of the moon from full to crescent, which it must do if the Copernican theory was correct. According to the Ptolemaic theory Venus would have to be a perpetual crescent. Galileo Galilei (1564 – 1642)

25. Observations consistent with Copernicus, inconsistent with Ptolemy.

26. Jupiter Has Moons Galileo Galilei (1564 – 1642) Galilean Moons – 4 Largest “moons” of Jupiter Io, Europa, Callisto, & Ganymede

27. 1632: "Dialogo Dei Massimi Sistemi” Dialogue on the Two Chief World Systems In Italian, Not Latin -- For the common people Two people, one representing the view of Ptolemy and other the view of Copernicus, present their arguments before an intelligent layman. Galileo Galilei (1564 – 1642) "Eppur Si Muove“ "(And, yet it moves!") The Pope Urban II thought that Simplico, the character who upheld the views of Ptolemy in the book, was a deliberate and insulting caricature of himself 1633: Trial by Church (threatened with instruments of torture), forced to recant views

28. 1633: Galileo is ordered to his house in Arcetri, under house arrest, where he remains for the rest of his life. The book remained on the index of forbidden books until 1822 Pope John Paul II finally gave an address that admitted that there had been errors in the treatment of Galileo by the church, in 1992. ASIDE: Contrast Galileo with Nicolas Steno (1638-1686), who laid the groundwork for the interpretation of the fossil record. See The Seashell on the Mountaintop by Alan Cutler.

29. Modern Scientific Method 1. Observations and Experiments Data which describes the physical world 2. Theory, Hypotheses, Models: -> Organize Facts from experiment & observations Unifying principles Make testable predictions

30. Creationism and Intelligent Design vs. Evolution. The example of gravity as a scientific theory: Newton’s Law c. 1700 AD Einstein’s theory of General Relativity c. 1916 Photon versus wave description of light The most interesting scientific questions to work on for a professional scientist are those we don't know the answer to. Interesting theories to work on are those which fail to explain an observation or fact. Many modern astronomers are deeply religious people.

32. The Astronomical Basis for Calendars The Earth rotates on its axis once a day. The Earth orbits the Sun with a period of about 365.242190 days The Moon orbits the Earth, such that the period between new moon and new moon is 29.5305 days These periods vary a little bit because of the gravitational forces exerted by the other planets and other factors. Every 4 years, we take into account the.242190 days by added a leap day, February 29. Otherwise we would keep slipping, and eventually January would be summer in the northern hemisphere, etc. Now, the thing is that there are NOT an integral number of months (29.5305 days) in one 365.242190 year. So if for example today is a new moon, next year it will not be.

33. SEASONS: Seasons are a result of the tilt of the Earth’s axis with respect to the plane of its orbit. Seasons ARE NOT the result of the Earth being closer to the Sun in summer, and farther in winter – in fact during winter in the northern hemisphere, we are closer to the Sun than we are in the summer.

40. The Gregorian Calendar (Christian, one we use) is based on the motion of the Earth around the Sun. The length and number of months have no connection to the motion of the Moon It is based on the Julian Calendar, which was introduced by Julius Caesar in 45 BC. He made Jan. 1 the start of the Year. During the middle ages, different groups in Europe adopted different start dates for the new years. In 1582, Pope Gregory reformed the calendar, which is basically what we use today. The French recognized a different pope for a while and had a different calendar.

41. The Islamic Calendar is based on the motion of the Moon, with no connection to the motion of the Earth around the Sun. Hijri Calendar, Based on the Qur'an. Used in many countries around the Gulf, e.g. Saudi Arabia. Purely lunar: 12 months, each with 29.53 days. Therefore the Islamic year has 12x29.53 = 354.36 days The Islamic year is shorter than the time it takes the Earth to go around the Sun. Thus, a particular Islamic month falls during different times of the year, e.g. Ramadan. Years are counted since the Hijra, which is is the time that Mohammed emigrated to Medina in AD 622. So AD 2009 is Islamic year 1430.

42. The Jewish and Chinese Calendars combine both, so years are linked to the period of the orbit of the Earth around the Sun, AND months are linked to the motion of the Moon around the Earth. 19 x365.24 = an integral number of 29.53 day months. Jewish Year: A "ordinary" year has 355 days, and 12 months. A "leap" year has 385 days and 13 months. The length of a particular month varies from year to year by a day, so that if New Year's Day (Rosh HaShannah) is, say, a new moon, then the first day of every month is a new moon. Years are counted since the creation of the world, taken to be 3761 BC. Thus 1998 is Jewish year 5759.

43. Mayan Calendar The ancient Mayans developed a complex and accurate calendar, which was adopted by other people in meso-america – Aztecs, Tolmec. Actually had THREE calendars, which they used at the same time: 1.The Haab Civilian calendar 18 months, 20 days each + 5 days to make 365 day years The 5 extra days were considered unlucky, days of mourning Did not count YEARS in the Haab calendar however 2.The Tzolkin Devine calendar, used for divinations two types of weeks, one with 13 days, the other with 20 days Each year was 260 days Years were not counted

44. Mayan Calendars, continued: 3.The Long Count Instead of years, the Mayan used the Long Count calendar system to keep track of historical events kin = 1 day uinal(1 uinal = 20 kin = 20 days) Tun(1 tun = 18 uinal = 360 days = approx. 1 year) katun(1 katun = 20 tun = 7,200 days = approx. 20 years) baktun(1 baktun = 20 katun = 144,000 days = approx. 394 years) pictun = 20 baktun = 2,880,000 days = approx. 7885 years calabtun = 20 pictun = 57,600,000 days = approx. 158,000 years kinchiltun = 20 calabtun = 1,152,000,000 days = approx. 3 million years alautun = 20 kinchiltun = 23,040,000,000 days = approx. 63 million years The Mayan calendar started on our August 11, 3114 BC. With Date: 0.0.0.0.0. Then date 13.0.0.0.0 is our December 21, 2012, or 12/21/2012.

45. This coincidence has caused some people to claim that the Mayan Calendar predicts the end of the world on December 21, 2012. But the Long Count calendar doesn’t end on 13.0.0.0.

47. Tycho Brahe (1546-1601) Danish nobleman Got drunk as a college student, lost his nose in a duel Built an observatory, Uraniborg, financed by King Frederic II Made extremely accurate Observations of the planets

48. Astronomiæ Instauratæ Mechanica: Tycho’s book about his instrumentation

50. Tycho made observations of the positions of the stars and planets that were 15x more accurate than what others had made He “beat down the errors” by repeating a particular measurement many times and averaging the result

51. Tycho’s cosmology Tycho found no parallax for the stars and concluded they are very far away He made measurements which neither the Ptolemaic model, nor the simple Copernicus model could explain. Earth stationary in center Sun and moon orbit the Earth Other planets orbit the Sun Stars orbit the Earth

52. Johannes Kepler (1564-1630) Worked as Tycho’s assistant Took Tycho’s observations when Tycho died and spent the next 29 years analyzing them First, he wrote “Mysterium Cosmographicum” The orbits of the 6 known planets were described By 5 “Pythagorian” polyhedra in spheres:

54. Eventually abandoned this model and came up with  Kepler’s Three Laws of Planetary Motion 1.Planets move in elliptical orbits (not circles), with the Sun at one focus.

55. 2. An imaginary line connecting the Sun to any planet sweeps out equal areas in equal time.. Area 2 Area 1 Planets move faster when near Sun

57. 3. The square of a planet’s orbital period is proportional to the cube of its semi-major axis. P 2 (years) = A 3 (astronomical units) 1 Astronomical Unit = The Earth-Sun Distance The farther out a planet is in the solar system, the longer it takes for it to go around the Sun.

59. Kepler’s Laws are empirical descriptions of the data. The don’t explain WHY the planets move as they do.

60. Isaac Newton (1642-1727) Bubonic Plague 1665: While home for 2 years with nothing to do he figured out Laws of motion Gravity

61. “Philosophiae Naturalis Principia Mathematica” The laws explained not only why planets move as they do, but why objects in general move as they do. Newton's First Law of Motion: Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it. speed: how many miles per hour velocity: speed and direction of motion acceleration: change in velocity, i.e. change in speed and/or change in direction of motion An object at rest stays at rest; an object in motion at a constant velocity stays moving at that velocity unless a force is exerted on it. Objects with mass have INERTIA.

62. Newton's Second Law of Motion : F = m a a = acceleration, change of velocity with time m = mass F = force Newton's third Law of Motion : For every action there is an equal and opposite reaction.

63. Law of Gravitation: F g = Force of Gravity

64. From kepler.nasa.gov

65. Forces of Nature : Gravity: very weak, but very long range. always attractive. always acts between any two masses Electro-Magnetism: Electric & Magnetic fields; light Result of charged particles, or magnets Long range Weak responsible for radioactive decay, e.g. beta decay -- n --> p + e + anti-neutrino the interaction of neutrinos Strong extremely strong on very short distance scales: only really important on scales of 10 -13 cm holds neutrons and protons in the nuclei of atoms together

66. James Maxwell (1831-1879) “Unified” Electricity and Magnetism  Electro-magnetic field, light Maxwell’s equations:

67. Glashow, Weinberg and Salaam got the Nobel Prize in Physics in 1979 for "unifying” Weak & EM forces and coming up with one theory which describes the "Electroweak Force" Grand Unified Theories : attempt to unify Electroweak and Strong forces Theory of Everything: one theory to describe all 4 forces Plus quantum mechanics

68. STRING THEORY everything is ultimately made of strings (sub-sub-sub atomic particles) How big are strings? Smaller than a Planck length, which is about 10 -33 centimeters or about a millionth of a billionth of a billionth of a billionth of a centimeter.

69. Strings vibrate Closed string Open string

70. In many string theories the Universe is 10 dimensional, with the "extra" dimensions COMPACTIFIED. All HS math geeks read a book called FLATLAND: A Romance of Many Dimensions, by Edwin A. Abbott (1884) FLATLAND: a "first person" account of life of a 2-dimensional society a radical named Arthur Square figures out that space is really 3 dimensional.

72. So what the string theorists say is that in ordinary life we think we live in 3 dimensions, and we have to think of ways to detect the other 7. The extra-dimensions in string theory are Calabi-Yau figures :

75. Crochet Calabi-Yau Figures